Wednesday, June 16, 2010

An object in motion tends to stay in motion with the same velocity unless acted upon by an unbalanced force. Unbalance can easily come in the way of a gentle sideways push during a sprint, such as that from Haussler yesterday which planted half a dozen riders including the Boy Racer himself straight down into the Wettingan straightaway like a bunch of toy pieces.

The sideways fall of a cyclist on his bike at rest can be simply modeled as an inverted pendulum, with the center of gravity inscribing a circle from θ=0 to θ=π/2 before hitting the ground. If g is the acceleration due to gravity for earth and r the height of the center of gravity, the acceleration of the fall in the tangential direction is then a function of the angle of fall - gsinθ - and the force is mgsinθ. Integrating acceleration for velocity, you'll find impact velocity at θ=π/2 as v = √(2g/r).

r = 0.8m is not a bad assumption for the center of gravity of a small sprinter like Boy Racer. Plug and chug and you find v = 4.95 m/sec ~ 10 mph!

But in the case of the sprint, Cavendish is not stationary but has an inherent velocity in the direction of the finish line of approx. 45 mph (assumed). The impact velocity can be considered a resolution of these two orthogonal velocities and what you get is a round about impact velocity of 46 mph or so.

This velocity is reduced to zero by the unyielding bitumen, but due to impact at an angle, its effect is slightly different from a more dangerous free falling vertical collision as the deceleration is spread out over more "seconds".

Looking at the video above, it seems like Cavendish lost most of his velocity in a little less than half a second after hitting flat on the ground on his back. I obtained 200 milliseconds using a stopwatch. Assuming constant deceleration, that would be about 100 m/s2. Which is 100/9.81 ~ 10 g's of impact force spread over the surface area of his back.

Is that a lot of force? Depends whom you talk to and which industry they belong to. But for the Boy Racer, it would really seem he were getting slapped hard on his back by a Sumo wrestler applying 10 times the former's body weight in force, roughly about 6 Kilo newton or 1300 pounds. Only for a fraction of a second, but certainly enough to have shocked him and given some nasty bruises to take home.

Well distributed G-forces can be handled by the body in several times more in magnitude than what the sprint crash has seen (see below). But the human head is slightly more complex and this sensitive system does not tolerate very high peak forces, especially in the rotational sense. I have put a perspective on the peak G forces on a head with helmet before. You should also read about Head Injury Criterion. Ride safe.

Is it Lightweight brand of wheels? Well that speaks a bit about its ability to withstand side loading doesn't it? The loading in terms of torsion must have been substantial as Cavendish was going down.

Recall not too long back when a Tour de France rider hit a dog that came across his path and the wheel crumpled like paper. I think he was going at about 10 mph.

Uhhh...that wheel got hit and ridden over by another bike on the rim edge and spokes as it was laying down at high speed when it flexed. No road wheel is going to survive getting it's spokes crushed and being torqued out of dish like that at even low velocities. I'm actually impressed the carbon rim too that much flex out of dish and bounced back round elastically.

**I'll see first hand evidence of a 32 spoke aluminum wheel doing this and then make the conclusion.**

Come on, you've never seen a crash-tacoed alloy rim once? ever?

Alloy rims get folded up dramatically in crashes all of the time - no rim is going to come out getting ridden over or plowing into a high obstacle at serious speed.

The failure mode of the wheel in crash situations of that type are largely irrelevant anyway unless it increases injury chances to the riders (ie carbon splinters, or similar cutting/puncture hazards etc). Race legal wheels are supposedly tested for minimum failure standards (impact resistance and failure behavior) as a result.

This isn't like the R-sys failure where a minor incident with the wheels lead to catastrophic failure of the whole wheel.

What I have seen and heard a lot of is simultaneous failure of multiple spokes causing cornering crashes in supposedly "bomb proof" alloy rims.

**The carbon rim didn't bend it snapped. I'd guess since the spokes broke as well then the tire would pull the broken rim back into a circle.**

Look at the wheel/rim in subsequent pictures, it's definitely partially fractured but something more than just a tire is holding it together - possibly some part of the weave still intacted or the core?

Jason : Let me reiterate. I have not yet seen a well built alloy FRONT wheel buckling due to the side loads of an impending fall. This to me is a rare situation. I have seen a carbon front wheel buckling here, in the video. I have also seen a similar wheel deforming when the rider hit a dog at less than 10mph. They make me laugh.

I can't think of any wheels, including MTB hoops that would not taco in that sort of case.

I do agree the survivability of some carbon hoops is quite suspect in other cases, say comparing Casars dog crash versus Burghardt's dog crash (the latter had complete wheel failure while Casar was able to ride away), but I've yet to hear of a case where an exceptional lateral failure of a carbon rim has actually caused a crash. In both cases they ate tarmac regardless of what the front wheel was doing.

When you've got a team car and neutral cars with spares its a value call on the wheel.

What makes me laugh is people training on carbon hoops or the proliferation of them in the cat 3/4 packs. But then I also snark at overly expensive bike gear in general.

with regards to the wheel buckling when it hit the dog, was this dramatic effect not a result of the rim being under 'tension' from breaking. (similar to getting a friend to stand on an empty coke can, without crushing it, then flicking the side which induces a complete crumpling)

It appears they covered meters 175 to 50 in 7 seconds, which would be 40 mph. I can't time it to better precision than that due to perspective. The strange thing is they seem to cover meters 100 to 50 extremely quickly, but that's probably a perspective trick.